We set the range of heavy particle mass to be \(10^{-2} \ {\rm GeV} \le m_\chi \le 10^9 \ {\rm GeV}\) . The lower mass \(m_\chi = 10^{-2}\)  GeV is used to avoid the warm DM consideration with PBHs [1]}, [2]}, [3]}. Conversely, because the semiclassical approximation used by Hawking to derive the evaporation spectrum fails at the Planck scale [4]}, [5]}, the upper mass should be lighter than the Planck mass, \(m_\chi < M_{\rm Pl}\) . The upper mass \(m_\chi = 10^9\)  GeV is sufficient to achieve our aim.
